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Algorithms 2017, 10(3), 74; doi:10.3390/a10030074

The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness

Department of Computer Science, Martin-Luther University, 06120 Halle-Wittenberg, Germany
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Received: 16 January 2017 / Revised: 20 June 2017 / Accepted: 22 June 2017 / Published: 27 June 2017
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Abstract

The discrepancy BR for an m × n 0, 1-matrix from Brualdi and Sanderson in 1998 is defined as the minimum number of 1 s that need to be shifted in each row to the left to achieve its Ferrers matrix, i.e., each row consists of consecutive 1 s followed by consecutive 0 s. For ecological bipartite networks, BR describes a nested set of relationships. Since two different labelled networks can be isomorphic, but possess different discrepancies due to different adjacency matrices, we define a metric determining the minimum discrepancy in an isomorphic class. We give a reduction to k ≤ n minimum weighted perfect matching problems. We show on 289 ecological matrices (given as a benchmark by Atmar and Patterson in 1995) that classical discrepancy can underestimate the nestedness by up to 30%. View Full-Text
Keywords: discrepancy; nestedness; BR; Ferrers matrix; Brualdi; Sanderson discrepancy; nestedness; BR; Ferrers matrix; Brualdi; Sanderson
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Berger, A.; Schreck, B. The Isomorphic Version of Brualdi’s and Sanderson’s Nestedness. Algorithms 2017, 10, 74.

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